Zero-field phase transition from nearly uniform in-plane to out-of-plane magnetization state in soft magnetic cylinders

Summary form only given. The equilibrium magnetization distribution and its stability in small magnetic particles is one of the old standing problems in the theory of micromagnetism. In a renewed attempt to describe the particle magnetization ground state the authors suggest a simple analytical approach for the description of zero-field magnetization vector distributions in soft magnetic disks, which allows one to calculate both the exchange and magnetostatic energy explicitly and analytically. It is based on the assumptions that the distribution of the variable magnetization along the disk thickness L (which is of order of the material exchange length) is uniform. They consider disks with the radius R ranging from a few microns up to the exchange length. The approach is based on the use of complex variables and the choice of appropriate trial functions. The magnetization distribution of an in-plane magnetized disk is modeled as a superposition of contributions from two skyrmions located outside the disk. The class of considered trial functions exactly minimizes the exchange energy functional, which is the most important energy contribution in particles of the size considered.